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首页> 美国政府科技报告 >OPTIMUM NONLINEAR CONTROL OF A SECOND ORDER NONLINEAR SYSTEM
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OPTIMUM NONLINEAR CONTROL OF A SECOND ORDER NONLINEAR SYSTEM

机译：二阶非线性系统的最优非线性控制

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A design technique of R. Oldenburger for the optimum nonlinear or predictor control of linear systems is herein extended to such control of a nonlinear system. This nonlinear system is composed of two major subsystems-a nonlinear controlled plant and a controller where the system output is that of the controlled plant. A nonlinear differential equation relates the system output variable to the input variable of the plant. The nonlinearity appears as an absquare (signed square) term in this system equation. The controller has two components, namely a decision making element or computer and a power element subject to saturation in the sense that the rate of change of its output is limited. This output is the input to the controlled plant. A major problem of predictor control design is the determination of the mathematical operations performed by the computer to achieve optimum transient response. An optimum transient is obtained when the controller brings the system to equilibrium in a minimum time after a disturbance has died out. Step changes in system load or the desired value of the system input are examples of such disturbances.nTo obtain optimum transients the computer is required to generate a control function dependent only on the system output variable, its first derivative, and the physical constants of the system. For optimum transients the controller power element operates in an on-off fashion, either at maximum or zero capacity, with the polarity of its output determined by -the sign of the control function. In the analytical derivation of the control function time is allowed to decrease from the instant at which equilibrium is reached for an optimum transient. By this technique it is proved that three distinct-types of optimum transients exist, classified according to the first and second derivatives of the system output variable as a function of time. In contrast to the case of the optimum nonlinear control of a second order linear system, where all transients are of the sane type and there is at most one change in sign of the second derivative of the controlled variable, there maybe as many as two changes in sign of this derivative for the second order nonlinear case. Non-ideal controllers are investigated, as when the positive and negative rates of change of controller output are unequal in absolute value, when the controller has a pure delay in switching, and when the controller contains a dead zone.

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